The Kalman Filter for Complex Fibonacci Systems

Abstract

This paper investigates the characteristics of the Kalman filter for a broad class of complex Fibonacci systems and represents an extension to the complex domain of the state estimation problem for the real-valued Fibonacci system. Complex Fibonacci systems are obtained by modifying the real-valued Fibonacci recurrence relation to include complex coefficients, control and noise inputs, and a noisy output-measurement equation. Analytic expressions for the Kalman filter’s steady-state gain and error covariance matrices are obtained, and it is found that for a broad subclass of these complex systems the elements of the matrices are functions of the golden ratio.